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## Question

So these are two more puzzles I found. It can be assumed that there are no tricks. The paths taken are the exact same length and route and the racers start at the exact same time.

Puzzle One

Two racers set out to race from point A to point B (a distance of 100 miles). They race (exact same route) and go different though uniform speeds. The difference between these two speeds is a prime number. After 2 hours The distance of the slower car from A was five times that of the faster car from B. The distances traveled and velocities are integers.

What are the speeds?

Puzzle two

Two men are racing. They start from a standing start and accelerate at a uniform rate. Joe covers the last quarter of the distance in 3 seconds. Bob covers the last third in 4 seconds, who won?

(for this question I will not respond to any answers without an explanation)

Please put Puzzle one or two before their respective sections in your response to avoid confusion. Also I found these problems without there solutions. I am pretty sure my answers are correct and the only answers, but crazier things have happened.

## Recommended Posts

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the slower racer is 80mi. from A..so the faster racer is 16 mi. from B..the slower racer traveled the 80 mi. at 40 mph...while the faster racer traveled 84 mi. at 42mph...a difference of 2mph...2 is a prime number.....so the answer would be..the slower racer was going 40mph...the faster racer was going 42mph

Edited by James8421

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The speeds are 40 mph and 42 mph.

The analysis shows the prime number must be even, so it's 2.

The rest is straightforward.

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wouldn't it end in a tie?

if it's a 12 mile race..break it down into thirds and quarters you have Joe running the last quarter (3miles) at 1 mile a second...and Bob running the last third (4miles) at 1 mile a second as well...so it seems they were running the same speed the whole time to the end..thems my thoughts

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Bob wins by a nose.

Analysis: recalling x = 1/2 a t2

Suppose the race is from x=0 to x=1. Then,

3/4 = 1/2 aj t12

1 = 1/2 aj t22

t2-t1 = 3

which gives aj = .063 ... as Joe's acceleration.

Whereas

2/3 = 1/2 abt12

1 = 1/2 abt22

t2-t1 = 4

which gives ab = .064 ... as Bob's acceleration.

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Let D be the race distance.

Then bob goes D/3 in 4 secs

S = ut + 1/2 at2

Lets say bob's speed at D/3 is u and acceleration is a, then he goes D/3 distance in 4 secs

D/3 = 4u + 8a ... (1)

Lets say he goes from D/3 to D/4 (a distance of D/12) in time "t", then

D/12 = ut + 1/2 at2 ... (2)

Then comparing 1 and 2, (divide equation 1 by 4)

u + 2a = ut + 1/2 at2

This means that t must be greater 1

Then this would mean that bob went from D/4 to finish in less than 3 secs while Joe went in 3 secs

Clearly, Bob is the winner

Edited by DeeGee

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Yeppers

Bob and prime=2

Now Ill leave this to you guys as I changed the first problem (and probably made it easier), because as I understand the original problem there is an answer for every prime below 50ish. but here it is word for word to see if u guys think im missing something.

"Two motorists set out at the same time to go from A to B, a distance of 100 miles. They both followed the same route and traveled at different, though uniform, speeds of an integral number of miles per hour. The difference in their speeds was a prime number of miles per hour, and after they had been driving for 2 hours, the distance of the slower car from A was five times that of the faster car from B. How fast did the two motorists drive?"

This is weird because the problem before this one specifically states integer variables and answer, this one doesnt. Also all the other problems ive bothered to solve so far have a single definite answer. So I am either missing something or ....

Edited by final

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... as I understand the original problem there is an answer for every prime below 50ish.

By my analysis, the prime had to be even, thus one unique answer.

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nope without the integer stipulation all hell breaks loose

p-------delta a---------Va--------------Vb-------------delta b-------- 5b-a=

1-------81.66666667-----40.83333333-----41.83333333-----16.33333333---- 0

3-------78.33333333-----39.16666667-----42.16666667-----15.66666667---- 0

5-------75--------------37.5------------42.5------------15------------- 0

7-------71.66666667-----35.83333333-----42.83333333-----14.33333333---- 0

11------65--------------32.5------------43.5------------13--------------0

13------61.66666667-----30.83333333-----43.83333333-----12.33333333---- 0

17------55--------------27.5------------44.5------------11------------- 0

19------51.66666667-----25.83333333-----44.83333333-----10.33333333---- 0

23------45--------------22.5------------45.5------------9-------------- 0

29------35--------------17.5------------46.5------------7-------------- 0

31------31.66666667-----15.83333333-----46.83333333-----6.333333333---- 0

37------21.66666667-----10.83333333-----47.83333333-----4.333333333---- 0

41------15--------------7.5-------------48.5------------3---------------0

43------11.66666667-----5.833333333-----48.83333333---2.333333333-----2.30926E-14

47------5---------------2.5-------------49.5------------1-------------- 0

Edited by final

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not the best formatting ive done but i think you get the idea

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...all hell breaks loose

I love it. My boss asked me what I was laughing about. He suspected I was a nerd. Now he knows. Plus I am tired.

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